Convergence of numerical schemes for convection–diffusion–reaction equations on generic meshes

Abstract

Using the gradient discretisation method (GDM), we provide a generic convergence of numerical approximations for convection diffusion model with non linear reaction term. The convergence of numerical schemes is proved based on a limited number of natural assumptions and properties. The validity of the proposed gradient scheme is examined using the finite volume method performed on different general meshes. We note that the numerical results indicate that a super-convergence property can be expected for the finite volume methods.

Keywords

• Convection and reaction problems
• A gradient discretisation method (GDM)
• Gradient schemes
• Existence of weak solutions
• Convergence analysis
• Mixed finite volume methods